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dc.contributor.authorPanda, B.S.-
dc.contributor.authorPandey, A.-
dc.date.accessioned2022-09-19T21:14:35Z-
dc.date.available2022-09-19T21:14:35Z-
dc.date.issued2022-09-20-
dc.identifier.urihttp://localhost:8080/xmlui/handle/123456789/4023-
dc.description.abstractFor a graph G =(V,E), a set M ⊆ E is called a matching in G if no two edges in M share a common vertex. A matching M in G is called an uniquely restricted matching in G if there is no other matching of the same cardinality in the graph induced on the vertices saturated by M. An uniquely restricted matching M is called maximal if M is not properly contained in any uniquely restricted matching of G. The minimum maximal uniquely restricted matching (Min-UR-Matching) problem is the problem of finding a minimum cardinality maximal uniquely restricted matching. In this paper, we initiate the study of theMin-UR-Matching problem. We prove that the decision version of the Min-UR-Matching problem is NP-complete for general graphs. In particular, this answers an open question posed by Hedetniemi [AKCE J. Graphs. Combin. 3(1)(2006) 1–37] regarding the complexity of the Min-UR-Matching problem. We also prove that this problem remains NP-complete for bipartite graphs with maximum degree 7. Next, we show that the Min-UR-Matching for bipartite graphs cannot be approximated within a factor of n1-ϵ for any positive constant ϵ >0 unless P = NP. Finally, we prove that the Min-UR-Matching problem is linear-time solvable for chain graphs, a subclass of bipartite graphs.en_US
dc.language.isoen_USen_US
dc.subjectBipartite graphsen_US
dc.subjectGraph algorithmen_US
dc.subjectMatchingen_US
dc.subjectNP-completeen_US
dc.subjectUniquely restricted matchingen_US
dc.titleOn the complexity of minimum cardinality maximal uniquely restricted matching in graphsen_US
dc.typeArticleen_US
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